The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in ratio [ISM Dhanbad 1994]
A) 1 : 2 B) 2 : 3 C) 2 : 1 D) 4 : 1
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The acceleration due to gravity on the planets will be in ratio. The option is A) 1 : 2.
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What we need to do is that we need to apply the universal law of gravitational . It states that
gravitation = GmM/R^2
That is : weight of an object on a planet is equal to the above stated equation
So m.g = GmM/R^2
So g = GM/R^2
When we further expand the equation
Mas = volume . Density ( because mass/volume is density )
While solving question we consider planets to be spheres . So volume = 4/3pi.r^3
So we can write the equation as :
G . 4.pi.R^3.density/R^2.3
So g= G.4/3.pi.R.density
Now to compare the g we will put them in a ratio
For planet one all the variable will consist of 1 along with them and for the second they will have a 2 .
So g1/g2= 4/3.G.pi.R.density/4/3.G.pi.R2.density2
So g1/g2=R1.density/R2.density
As the ratios have been provided earlier we will just put the values in the variables :
g1/g2= 4.1/1.2
g1/g2= 2:1
gravitation = GmM/R^2
That is : weight of an object on a planet is equal to the above stated equation
So m.g = GmM/R^2
So g = GM/R^2
When we further expand the equation
Mas = volume . Density ( because mass/volume is density )
While solving question we consider planets to be spheres . So volume = 4/3pi.r^3
So we can write the equation as :
G . 4.pi.R^3.density/R^2.3
So g= G.4/3.pi.R.density
Now to compare the g we will put them in a ratio
For planet one all the variable will consist of 1 along with them and for the second they will have a 2 .
So g1/g2= 4/3.G.pi.R.density/4/3.G.pi.R2.density2
So g1/g2=R1.density/R2.density
As the ratios have been provided earlier we will just put the values in the variables :
g1/g2= 4.1/1.2
g1/g2= 2:1
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